Spiral inductors are important components of many high-frequency circuits such as voltage controlled oscillators, low noise amplifiers, mixers, and other components. Generally, a high quality factor, Q, is desirable for high performance. A high quality factor translates to lower phase noise in voltage controlled oscillators and a lower noise figure in low noise amplifiers.
The quality factor is a function of energy stored, which may be defined by the difference between peak magnetic energy and peak electric energy, and the energy loss in one oscillation cycle. The quality factor is limited by energy stored in parasitic capacitance, ohmic loss in the inductor windings, and energy loss in the substrate. Resistance in the inductor windings increases with frequency due to skin effect and proximity effect which causes significant degradation in the inductor's quality factor.
The skin effect causes AC current to crowd towards a surface of an inductor winding due to self induction. The proximity effect causes AC current to crowd towards the outer edges of parallel lines due to mutual induction. The skin effect and proximity effect are caused by eddy currents which are induced by time-varying magnetic field. Eddy currents flow in a direction that produces an opposing magnetic field. Eddy currents combine with applied currents and result in current crowding on edges of lines.
Prior approaches of increasing the width of an inductor winding had limited benefits since most AC current flows along the sides of the winding due to the lateral skin effect and proximity effect. Also, the utilization of multiple metal levels for winding had limited benefit because most AC current flows through the top surface of the top metal and the bottom surface of the bottom metal in an inductor metal stack.